Four layer anti-reflection coating

ABSTRACT

A multi-layered anti-reflection coating for use with a glass substrate includes four layers of material, the first layer furthest from the substrate having an optical thickness of a preselected design wavelength, lambda o in the range of 0.260 lambda o &gt; Nld1 &gt; 0.230 lambda o and an index of refraction in the range of 1.35 to 1.62. The second layer having an optical thickness in the range of 0.520 lambda o &gt; N2d2 &gt; 0.400 lambda o and an index of refraction in the range of 2.00 to 2.30. The optical thickness of one of the third and fourth layers is in the range of 0.500 Tau o &gt; N d &gt; 0.250 lambda o while the optical thickness of the other layer of the third and fourth layers is in the range of 0.250 lambda o &gt; N d &gt; 0.060 lambda o. The third layer has an index of refraction in the range of 1.56 to 1.72 and the fourth layer closest to the substrate has an index or refraction in the range of 1.35 to 1.62. The optical thicknesses of the layers can be varied to compensate for any variations from the theoretical design index of refractions.

United States Patent 11 1 Sumita 1 Dec. 25, 1973 [75] lnventor:

[73] Assignee: Minolta Camera Kabushiki Kaisha,

Minami, Osaka, Japan [22] Filed: Nov. 6, 1972 [21] Appl. No.: 304,140

llaruki Sumita, Osaka, Japan Primary Examiner-Ronald L. WibertAttorney-Harold L. Jackson et al.

[57] ABSTRACT A multi-layered anti-reflection coating for use with aglass substrate includes four layers of material, the first layerfurthest from the substrate having an optical thickness of a pre selected design wavele n gth in the range of 0.260 M N ,d, 0.230 A0 and anindex of remtion in theTange of 1.35 to 1.62. The second layer having anoptical thickness in the range of 0.520 A N d 0.400 A and an index ofrefraction in the range of 2.00 to 2.30. The optical thickness of one ofthe third and fourth layers is in the range of 0.500 A) Nd 0.250 A0while the optical thickness of the other layer of the third and fourthlayers is in the range of 0.250 A Nd 0.060 A The third layer has anindex of refraction in the range of l.56 to l.72 and the fourth layerclosest to the substrate has an index or refraction in the range of l.35to 1.62. The optical thicknesses of the layers can be varied tocompensate for any variations from the theoretical design index ofrefractions.

20 Claims, 16 Drawing Figures 52 /MZ- M!) PATENIEU ntczs ms SHEET 0F 6MM 45mm (12 m) m2 (A 75% 5a) PATENIED BECZ-S ms SHEET 5 or 6 fzf 11.

WV! m/an/ [2111) wwm WAVE m/ars [72711) PATENTEDUEE 25 m5 SHEET 6 OF 6500 IVAVK [fl/67b 62 m) l FOUR LAYER ANTI-REFLECTION COATING BACKGROUNDOF THE INVENTION 1. Field of the Invention The present invention isdirected to an anti-reflection coating for a substrate to minimize thereflectance of applied energy and more particularly, to four-layeranti-reflective optical coatings.

2. Description of the Prior Art There have been numerous attempts toprovide various anti-reflective coatings for reducing the reflection ofenergy off of a substrate. In recent years the primary emphasis in theoptics field has been upon reducing the reflectance of light from glasssubstrates in the visible spectrum of 400 to 700 nanometers. A largenumber of solutions have been offered to decrease the Fresnel reflectionof optically transparent material especially in optical lenses used incameras and the like.

The use of a single and double layers of antireflecting coatings havebecome extremely popular. Since the visual spectrum extends over arelatively wide wavelength band, and a single layer is principallydesigned to nullify reflectance at a single design wavelength, its usehas not provided satisfactory results over the entire visual regionespecially for low index glass having a refractive index from 1.45 to1.9.

Three layer anti-reflection coatings such as in the U. S. Pat. No.3,185,020 and U. S. Pat. No. 3,604,784 have greatly improved the desiredoptical characteristics over the single and double layer coatings.Generally the first layer next to the air is designed to minimize thereflectance and has a low refractive index with an optical thickness ofone-quarter wavelength. As is well known to those skilled in the art,the optical thickness is the physical thickness multiplied by the indexof refraction of the material. Generally the optical thickness isnormally described in fractions of the wavelengths of the design lightray through which the coating is to be used. Frequently, the designwavelength will be picked as nanometers.

in the normal three layer anti-reflection coating, the second layer willhave a high refractive index, NH, and will be one-half wavelength inoptical thickness. A half wavelength optical thickness does not alterthe optical characteristics of the other layers and therefore has noeffect on the residual reflectance; however, it will broaden or expandthe anti-reflection effect of the total coating on both sides of thedesign wavelength. The last layer adjacent the substrate will have amedium refractive index, NM, and generally an optical thickness thatwill be of a three-quarter wavelength or one-quarter wavelengththickness. Generally, this third layer next to the substrate will act asa matching layer between the first two layers and the substrate in orderto maintain the anti-reflection characteristic of the design.

The prior art has further utilized four layer antireflection coatingssuch as disclosed in U. 8. Pat. No. 3,432,225 and U. S. Pat. No.3,565,509. Generally these coatings have been designed to produce anequivalent thickness layer which consists of two or three thin layersthat work as a half wavelength high refractive index or a quarterwavelength medium refractive index layer in the anti-reflection coating.Frequently, the individual layers will be extremely thin and very oftenonly 300 angstroms thick. Manufacturing tolerance problems are arecurrent problem with the use of these thin individual layers and thefinal summation of their effect is simply to provide an equivalentwavelength layer in the design.

Another approach has been to use two' separate materials of differentrefractive indices that are coevaporated to secure the arithmetic meanrefractive index or a continuously changing refractive index withrespect to the thickness. The continuously changing refractive index canbe accomplished by changing the evaporation rate of the two materialswith respect to the desired thickness. This method, for example, isdisclosed in U. S. Pat. No. 3,176,574. As may be readily understood,this method requires precise control of evaporation material andtechnique.

The use of four layers of different evaporated materials providessuperior results over that of the triple layer structure. An example ofthis four different material coating is disclosed in U. S. Pat. No.3,463,574. Since quarter or half it is necessary to use four materials,there are production problems relating to the evaporation and theprecise control of the layer thickness and the design is still limitedto various refractive index combinations corresponding to the substrate.In addition, the layered structure has a tendency to fractionalize andit is often found in production that the available material does notmaintain or even correspond to its purported theoretical refractiveindex.

In the commercial production of anti-reflection coatings, a choice ofmaterial having a high or medium index of refraction generally requiresa metal oxide which in commercial use is often found to be inhomogeneousand unstable in its refractive index. This is also true with highindexed fluorides such as CeF LaF and NdF in the U. S. Pat. No.3,565,509 a multi-layer antireflection coating using a combination ofonly two materials is provided. This is accomplished by using asymmetrical array of layers to obtain an equivalent layer having anequivalent index of refraction and an equiva lent thickness. Thefundamental period must be symmetrical about the center of the period.The properties of the one period equivalent layer are such that in orderto obtain the optimum anti-reflection band width, the thickness of thethird layer from the substrate should be less than the sum of thethickness of the thin layer next to the substrate plus a halfwavelength.

Basically, the designs of the anti-reflection coatings in the prior arthave relied upon the classical solution utilizing a quarter wavelengthsystem as represented by the Jupnik's solution, set forth in Physics ofThin Film, volume 2, p.272, by G. Hass and RE. Thun, Academic Press.Using this approach in a Jupnik four layer anti-reflection coatingstructure having for exam- P's an e q l i s q s of Mus 5. fractiveindices must be proportionately represented by N,N =N; N,N,' where Nrepresents the index of refraction and N would be the index ofrefraction adjacent the substrate having an index of refraction of N,.N, is the index of refraction of the medium such as air.

Other designs with the classical quarter wavelength structure producesimilar restrictions that effect the utility and flexibility of ananti-reflective coating. In particular, material of high and middlerefractive indices frequently have refractive indices that are notconsistent and readily applicable to a, production line technique.

' In addition, the reflectance curves for various wavelengths aresymmetrical with respect to l/M, where A is the design wavelength. Inthe classical design, this produces a minimum reflection at A and atjtsinteger magnified wavelengths, and any refractive index deviationscannot be adequately compensated by variations in the optical thickness.

SUMMARY OF THE INVENTION The present invention provides a four layerantireflection coating which provides flexibility in varying opticalthicknesses of the layers to compensate for deviations in the refractiveindices particularly in the relatively high and medium indices ranges,that is indices generally having a value above 1.6. This is accomplishedby providing a four-layer anti-reflection structure that is not limitedto the restrictions of the classical quarter wavelength design butenables the optical thickness of the various layers to be altered asrequired to maintain the low reflectance that is theoretically possiblewith theoretical material having a consistent index of refraction.

The first layer of coating which is next to the medium, that is,generally the air coating inner face and the fourth layer which is nextto the substrate, which is generally glass, will generally have arefractive index range between 1.35 and 1.62. Some of the materialswhich are capable of being utilized on the first and fourth layers withtheir refractive indices in parentheses are MgF, (1.385), SiO, (1.46),ThF, (1.5), LaF (1.56), Na;, (AlF (1.35), A1 0 (1.62), and CeF (1.615).Other materials having the desired optical characteristics and arefractive index between 1.35 and 1.62 can also be utilized.

The second layer relative to the top of the antireflection coating has arelatively high refractive index generally equal to or between NH 2.00and 2.30. A number of materials can be utilized and illustrative of suchmaterials are the following with their index of refraction inparentheses: CeO (2.30 2.00), ZrO, (2.10 2.00), TiO, (2.30 2.00), Ta O(2.30 2.00), ZnS (2.30 2.20), and Th0, (2.20 200).

Finally, the third layer from the top of the antireflection coating willhave a refractive index equal to or between NM 1.72 and 1.56, andillustrative of materials which can be utilized are the following withtheir index of refraction in parentheses: A1 0; (1.65 1.56), MgO (1.72),CeF (1.62), LaF (1.59), NdF (1.60), BeO (1.60), ThOH (1.70). lnO-(1.8-1.9) and a mixture of MgO and A1 0 (1.72 1.65).

The range of optical thickness for the present invention is set forth asfollows:

0.260 x Md, 0.230 A0 0.500 1 N d 0.060 M The optical thickness of thethird and fourth layers are set forth in the above optical thicknesstable over their broad applicable range; however, as a result of thenon-quarter design approach of the present invention, it is possible tooffer alternative solutions or design parameters to the third and fourthlayers that can be summarized as follows. When the third layer isthicker than 1.0/4 then the fourth layer will be thinner than lei/4,that is 0.500 M N d 0.250 A0 and 0.250 M N d 0.060 1. In thealternative, when the third layer is thinner than A0/4, then the fourthlayer will be thicker than Ari/4, that is, 0.250 A, N d 0.060 A.) and0.500 M N d 0.250 A.

While the specific embodiments of the present invention are illustratedin the visual spectrum range'of 400 to 700 nanometers, it should berealized that the broad principles of the present invention are alsoapplicable in the ultraviolet and infrared wavelength range withappropriate adjustments of the layer film materials, refractive indicesand substrates.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a schematic diagram of ahypothetical coating;

FIG. 2 is a schematic diagram of the reflections from a multi-layeredcoating;

FIG. 3 is a vector diagram;

FIG. 4 is an example of the vector coordinate system;

FIG. 5 is a graph showing the reflectance of an antireflection coatingof TABLE 1 of this invention;

FIG. 6 is a cross section of the anti-reflection coating of TABLE 3;

FIG. 7 is a reflectance graph of TABLE 3;

FIG. 8 is a reflectance graph of TABLES 4 and 5;

FIG. 9 is a reflectance graph of TABLES 6 and 7;

FIG. 10 is a cross section of the anti-reflection coating of TABLE 8;

FIG. 11 is a reflectance graph of TABLE 8;

FIG. 12 is a reflectance graph of TABLES 9 and 10;

FIG. 13 is a reflectance graph of TABLES 1 1 and 12;

FIG. 14 is a reflectance graph of the coating of U. S. Pat. No.3,463,574 shown in TABLE 13;

FIG. 15 is a reflectance graph of the coating of U. S. Pat. No.3,432,225 shown in TABLE 14; and

FIG. 16 is a reflectance graph of the coating of U. S. Pat. No.3,565,509 shown in TABLE 15.

DESCRIPTION OF THE PREFERRED EMBODIMENT As may be appreciated by thoseskilled in the art, the use of various metal oxides and fluorides asoptic coatings frequently do not have a stable refractive index nor ahomogeneous structure. Solutions and compounds of these materials aresubject to a number of variables such as the starting stoichiometricstructure of the material, the equipment used and the evaporationtechniques. In commercial production it is extremely difficult tomaintain the precise and consistent control of the various layers of ananti-reflection coating to maintain the final result within the designparameters of the anti-reflection coating.

In contrast, a low index of refraction material such as MgF has arelatively stable index of refraction of 1.385 even with film layerthicknesses thinner than A0/2 while also maintaining a homogeneousconstituency.

The following derivations in conjunction with FIGS. 1 4 will helpexplain the advantages of the present invention over that of theclassical quarter wave design utilized in the prior art.

In the following equations:

p is the reflection coefficient and is a complex number from which thereflectance R is derived as follows:

the layer twice as disclosed in FIG. 2, and is expressed by,

p=g 217mm.

N is the refractive index and d is the physical thickness.

W is the Fresnel coefficient at the boundary and is defined by,

Wi (Ni-l Ni)/(Ni-l Ni) where the suffice i represents integer number atthe boundary of substrate p =W In case of Glass-Air interface WI 0.04,because the refractive index of the glass is assumed to be N,=l.5.

Now, p is derived from the following recurrence formula,

pi= (pi 4 ai/(1+ win. w 4) where p 0.04, W, 0.], therefore, thedenominator in Equation (3) can be assumed to be 1 without introducingany significant error, whereby the final reflection coefficient p,, canbe written as Pa s (fi4 B3 B2 BI) 4, (B3 fl2 Bt) a '(B2+Bt) z fii i-This equation is graphically represented in FIG. 2 where the reflectedrays from the layer boundaries are simply added up and contribute to thetotal reflectance if we ignore any mutual interference effects.

As can be seen in H6. 3, every term can be considered as a vector, V VThe summation of these vectors will give the final reflectioncoefficient p,,. If these vectors form a closed loop, the finalreflection p will be zero.

This can be more easily understood when the vectors are shown in thecomplex plane. Referring to FIG. 4, the Absessa is the Real Axis and thephase angle B is measured from this axis in a counter-clockwisedirection.

ln order to solve Equation (4) having a large number of variables, it isnecessary to eliminate as many variables as possible, and accordinglythe following assumptions are made:

I. The first coating layer next to the air or medium will contribute tothe total anti-reflection effect and is set at, N, d, M4.

2. The second coating layer will be utilized to increase wavelength bandof the design and will be, N-gdg These assumptions produce the followingphase factors:

i M E BL M) Ngdg= 2'.

Therefore, setting Equation (4) to the optimum condition of zero andsubstituting Equation (5) the equation is reduced to:

The solutions are sin (B -H3 4/ s) sin 33- If we define the refractiveindex Ws as calculated by Equation (2), then 3;, can be obtained fromEquation (7) and B, can be calculated from Equation (8).

The inventive design shown in TABLE 1 has been derived by this processwith a substrate refractive index of Ns 1.52.

The first layer is N 1.385 and Ma, M4. and the second layer is N- 2.05and N d A12.

If we choose N 1.58, N, 1.385, then two solutions are obtained:

B3 5 and B4= (4m) zyi 2442o' These solutions are shown in the Vectordiagram of FIG. 3.

The length of each vector is related to the Fresnel coefficient which isa simple function of the refractive index. The direction B of eachvector is a function of the optical thickness. The vectors from eachlayer are shown by V,, V

lf vector V, terminated at the origin 0, then we obtain p, 0 and thus R0.

If the first and the second layers have A/ 4 thickne s s then [3,, art17; are the integer multiples of 1r, and therefore, vector V,,, V, andV, will be on the real axis.

Starting from vector V, on FIG. 3 to equate p, to zero, then vectors Vand V must return to zero. These vectors have the respective Fresnelcoefficients W, and W Using a circle having a radius W, with its centerat vector V and another circle of radius W,, with the center at 0, it ispossible to find two intersections at a symmetrical position withrespect to the real axis. lf V and Oare respectively connected, we candefine V and V When these two circles intersect on the real axis thereis only one solution, and the optical thickness will be M4 and )t/4.This is the classical .lupniks solution, and the optical thicknessstructure will be A/4, M2, )t/4, A/4. g

With the classical solution of the quarter wavelength system, the phaseangle B will be an integer multiple of 1r and the vectors will terminateon the real axis only. The length of the vector is related to theFresnel coefficient which in turn is a simple function of the refractiveindex, and is independent of the film thickness.

Therefore, in order to terminate the vector summation at the origin 0,the refractive indices of the coating will be restricted by therelationship N,N,=N VN,N,,. Variations of the classical solution willhave other similar refractive index restrictions.

With the present invention we introduce a nonquarter structure for thethird and fourth layers, and their vectors do not end on the real axis,but rather in the imaginary plane. The Fresnel coefficients can beadjusted by the phase angle in order to terminate the V vector at theorigin.

With the present invention two separate solutions are always possible tomeet the design requirements, that is:

I. When the third layer is thicker than 11/4, then the fourth layer willbe thinner than M4, and

2. when the third layer is thinner than 11/4, then the fourth lagr willb e thicker th a n AM As can be readily understood, the flexibility ofthe present invention in permitting optical thickness compensation tomeet the design parameters provides the optical designer with asignificant advancement in the art.

The explanation of the present invention to this point has been for anywavelength M, to p r oduce p,, 0. However, for our prime application inthe visual spectrum, it is desirable to minimize the reflectance in asbroad a range as possible, e.g., the entire visual spectrum range 400700 nm.

Utilizing the above approximate solution, and a computer, the followingdesigns were optimized. The technique utilized with the computer is theso-called damped least square method. That is to minimize the quantitydefined by:

Due to the non-quarter wavelength design, iii; possiand R* x is a ble tocompensate the reflectance with respect to refractive index variationsby thickness adjustments of the layers of the third and fourth coating.While in any optical design there will be optimum values for arelatively high refractive index layer and a relatively middle rangerefractive index layer for a particular substrate it has been oftenfound in practice that the particular materials are not available orpractical commercially or the subsequent evaporated film layer will havean index of refraction which will fluctuate from the theoretical value.With the present invention, it is possible to compensate for thesevariations and produce a commercial anti-reflection coating.

A further advantage of the present invention is that its designs havethree minimized reflections for a glass substrate with an index ofrefraction between 1.42 and 1.72 across the wavelength band of 400 to700 nanometers. This inventive design perrnits the extreme edges of thewavelength band to have a minimal residual reflectance as compared tothat of the prior art. This characteristic of the present invention isimportant particularly in color photography and also in wide anglephotographic lenses. In a wide angle lens, when the incident angleincreases, the reflectance will increase across the entire region andthe reflectance curve with respect to the wavelength will shift towardsa shorter wavelength.

Finally, the present invention can be accomplished with only threeseparate conventional materials.

The following examples are illustrative of the present invention:

TABLE I Refractive Index Optical Thickness (in design wavelength) 1.000Incident light side medium 1.385 0.250

2.050 0.510 1.580 0.333 1.385 0.089 1.520 Substrate glass Referring toFIG. 5, a percent of reflectance versus wavelength curve is shown forthe design in TABLE l. Curve 10 is for a 0 incident angle while curve 11is for a 40 incident angle.

The following TABLE 2 discloses a classical three layer coating designand is presented for comparison value:

TABLE 2 Refractive Index O.T. 1.000 Incident light side medium 1.3850.250 2.050 0.500 1.630 0.250 1.520 Substrate glass In FIG. 5, line 12represents the 0 incident angle curve for the design of TABLE 2 whileline 13 represents the 40 incident angle curve for the same TABLE 2. Itshould be noted that the residual reflectance particularly at the longerwavelengths between 600 and 700 nanometers is considerably decreasedwith the design of TABLE 1 and this is of particular importance in colorphotography.

A cross sectional diagram is disclosed in FIG. 6 showing a secondembodiment of the present invention. In this design the substrate 20 canhave an index of refraction that will vary from 1.42 to 1.62. Thecoating layers are shown successively as 21, 22, 23, and 24. The designparameters are set forth in the following TABLE Substrate glass Thereflectance curve of the second embodiment of the present inventiondisclosed in TABLE 3 and FIG. 6 is shown in FIG. 7 for various substrateindices. Curve 31 corresponds to a substrate Ns 1.42; curve 32corresponds to a substrate Ns 1.52; and curve 33 corresponds to asubstrate Ns 1.62. The incident angle for each of the above curves is 0.As can be seen from these curves, the residual reflectance is below 0.4percent while at the extreme edge it is still below 1.4 percent.

If the index of the relatively high (NH) layer is modified, that is thesecond layer, it is possible by changing the various thicknesses of thelayers to maintain an acceptable anti-reflection coating. Referring toFIG. 8, the curve 32 of FIG. 7 is repeated as curve 40 where N (NH)equals 2.15. Curve 4! is the resultant thickness compensated reflectioncurve when N, has been changed to 2.00. The adjusted thicknesses and thedesign parameters for the coating of curve 41 is disclosed in TABLE 4below. Curve 42 is another thickness compensated reflection curvewhen-N, has been changed to 2.30, the adjusted thicknesses and thedesign parame ters are disclosed in TABLE 5.

TABLE 4 R. l. O. T. M (change of thickness) Medium 1.000 incident side1.385 0.241 0.004 2.000 0.442 0.01 8 1.630 0.173 +0.007 1.385 0.455+0.037 1.520 Substrate TABLE 5 R. I. O. T. Ad

Medium 1.000 incident side 2.385 0.250 +0.005 2.300 0.484 +0.024 1.6300.219 +0.053 1.385 0.356 0.062 1.520 Substrate As can be seen from theabove FIG. 8, even when the high refractive index layer is changed inits refractive index from an NH 2.00 to a NH 2.30, the present inventionpermits a four layer optical thickness adjustment that is capable ofmaintaining a low reflectance in the order of 0.35 percent across thegeneral region of the spectrum and about a 1 percent reflectance at theextreme visual ends of the spectrum.

Referring to FIG. 9, an additional embodiment of the present inventionis disclosed. Utilizing the design parameters presented in the aboveTABLE 3 and having the medium index layer or coating N vary in its valuefrom 1.63 to a new value of NH 1.56 and further varying to NM 1.70 itcan be seen that the four layer coating thicknesses can still beadjusted to maintain the low residual reflectance of the original designIn FIG. 9, curve 50 is equivalent to curve 32 of FIG. 7 with a NM equalto 1.63. Curve 51 shows the resulting residual reflectance after athickness adjustment of the four layers for NM 1.56. The final designparameters and the adjustments are disclosed in TABLE 6 below. Curve 52shows an additional adjustment when NM 1.70 and the design parametersare presented in TABLE 7.

TABLE 6 R. 1 O. T. M

Incident 1.000 side medium 1.385 0.246 +0.001 2.150 0.481 +0.021 1.5600.174 +0.008 1.385 0.389 +0.029 1.520 Substrate TABLE 7 R. 1. O. T. M

Incident 1.000 side medium 1.385 0.243 0.002 2.150 0.430 0.030 1.7000.186 +0.020 1.385 0433 +0015 1.520 Substrate Thus even while therefractive index of the layer in the medium range changes from 21 NM of1.56 to 1.70, the anti-reflection coating was still capable ofmaintaining a very low residual reflectance of less than 0.22 percentacross the general region of the band width while at both ends of thevisual spectrum the reflectance is kept within 1 percent due to theinherent flexibility of the design in permitting an adjustment in thethickness of the coating layers.

A third embodiment of the present invention is disclosed in FIG. 10 andthe parameters of the design are presented in TABLE 8 below. Thesubstrate 60 can have a refractive index between 1.56 and 1.72 and thefour layers of coatings are respectively numbered 61, 62, 63, and 64.

TABLE 8 Refractive Index 0. T. 1.000 Incident side medium 1.385 0.2502.250 0.510 1.610 0.333 1.385 0.089 1.620 Substrate FIG. 11 disclosesthe percent of refraction with respect to wavelength for the design ofTABLE 8. In FIG. 7, curve 71 corresponds to a substrate N, 1.56; curve72 corresponds to N,= 1.62; and curve 73 corresponds to N 1.72. As canbe seen, the residual reflections are about 0.4 percent across the broadcentral region of the visual spectrum and less than 1.6 percent at theextreme ends of the visual region even though a widely distributedsubstrate index was utilized.

FIG. 12 discloses the percent of reflection after the coating designpresented in TABLE 8 was modified to adjust for a change in index from anominal value of NH 2.25 to values of NH 2.05 and NH 2.30. Curvecorresponds to the value of NH 2.25; curve 81 corresponds to NH 2.05;and curve 82 corresponds to NH 2.30. TABLE 9 presents the correcteddesign parameters associated with curve 81 while TABLE 10 discloses thedesign parameters associated with curve 82.

TABLE 9 R. I. O. T. Ad

Incident 1.000 side medium 1.385 0.249 0.001 2.050 0.509 0.001 1.6100.347 +0.014 1.385 0.074 0.015 1.620 Substrate TABLE 10 R. l. O. T. Ad

Incident 1.000 side medium 1.385 0.253 +0.003 2.300 0.514 +0.004 1.6100.331 0.002 1.385 0.094 +0.0O5 1.620 Substrate As can be seen from theabove tables, when the high index NH is changed from 2.05 to 2.30, thepresent invention still permits the residual reflectance to bemaintained less then 0.28 percent across the general visual region, andat the longer wavelength reflectance is maintained at less then 1percent and at the shorter wavelength of the spectrum it is stillmaintained within 2 percent by the appropriate adjustments in thethickness of the layers.

FIG. 13 discloses the effects of variations in a middle range index ofrefraction, NM, in the third embodiment presented in TABLE 8 above. Ifthe original value of NM equals 1.61, and it is modified to NM 1.57 orto NM 1.70, the residual reflectances can still be maintainedapproximately as low as the original design by appropriate adjustmentsin the thickness of the four layers. Referring to FIG. 13, curvediscloses the reflectance curve for NM 1.61; curve 91 shows thereflectance curve when NM is modified to 1.57; and curve 92 shows thereflectance curve when NM is modified to 1.70. TABLE 11 below disclosesthe parameters associated with curve 91 while TABLE 12 below disclosesthe design parameters associated with curve 92.

TABLE 1 l R. l 0. T. Ad

Incident 1.000 side medium 1.385 0.253 +0.003 2.250 0.513 +0.003 1.5700.336 +0.003 1.385 0.094 +0.005 1.620 Substrate TABLE 12 R. l. O. T. M

Incident 1.000 side medium 1.385 0.252 +0.002 2.250 0.513 +0.003 1.7000.321 0.0l2 1.385 0.076 0.013 1.620 Substrate As can be seen from F 1G.13, the residual reflectance is kept under 0.25 percent across thegeneral visual spectrum while at the longer wavelength end it ismaintained below 1 percent and at the shorter wavelength end it ismaintained within 1.8 percent by the appropriate adjustments in thethickness of the four layer coatmgs.

In order to more readily appreciate the advantages of the presentinvention over the prior art, TABLE 13 has been prepared disclosing aclassical four layered structure design that is described in U. S. Pat.No. 3,463,574. The reflection characteristics of this antireflectionfour layer coating is disclosed in FIG. 14 as curve 100. I

If one of the high index layers varies in its design refractive indexfrom NH 2.07 to NH= 2.00, the reflection curve will vary as shown incurve 101. In the alternative, ifthe same high index layer varies to NH=2.30, the reflection curve is presented by curve 102.

TABLE 13 Refractive Index 0. T. 1.000 Incident side medium 1.380 0.2502.070 0.250 2.190 0.250 1.730 0.250 1.510 Substrate In the alternative,if the same TABLE 13 has its medium index layer NM equal to 1.73 variedrespectively to 1.63 and 1.77, the corresponding reflection curves willbe disclosed respectively by curve 103 and curve 104. A careful analysisof FIG. 14 discloses that the degree of reflection varies considerablywith variations in the indices of the high and medium index ofrefraction layers. Due to the fundamental quarter wave optical thicknessstructure from which the optical design is derived, there are novariables left in the design to compensate for index variations byadjusting the thicknesses. For this reason, it is impossible to maintainthe original reflectance design by compensating adjustments in thevarious layer thicknesses. This limitation should be compared with theabove examples of the three embodiments of the present invention thatdisclose a flexibility of design to meet any variations in the indicesof refraction which are quite common'occurrences in production.

TABLE 14 Refractive Index 0. T. 1.000 Incident side medium 1.380 0.25002.080 0.5000 1.380 0.0606 2.080 0.0532 1 .520 Substrate to a refractiveindex of 2.30, the resultant reflectance curve is disclosed in FIG. 15as curve 111. As can be seen from the curve, there is a drastic increasein percent of reflection at both ends of the visual spectrum. An effortwas made using the non classical design theory of the present inventionto widen the reflectance curve so that the reflectance mean reaches aminimum by adjusting the thickness of the coating. The optimum adjustedthickness that was computed by the non classical approach is shown ascurve 112. However, as can be seen by comparing the curves, there wasnot any substantial improvement. The reason why the reflectance curvecannot be improved is that while the design may appear on the surface asa non quarter structure, it is effectively a triple layer classicaldesign since the two layers next to the substrate layer work effectivelyas a single layer in the classical design.

A final third example of a prior art four layer antireflection coatingis provided to further emphasize the value of the present invention.

TABLE 15 Refractive Index 0. T. 1.000 Incident side medium 1.380 0.25002.080 0.5290 1.380 0.0790 2.080 0.0581 1.520 Substrate TABLE 15discloses the design parameters of U. 8. Pat. No. 3,565,509. Referringto FIG. 16, the reflectance curve of TABLE 15 is presented as curve 120.If the high index layer, that is the second layer N, with respect to theincoming light medium boundary has its refractive index modified to NH2.30, the resultant reflectance curve for TABLE 15 becomes curve 121. Asa result of this variation in the index of refraction, the reflectanceat the ends of the visual spectrum is remarkably increased. Again, sincethe structure has a superficial appearance of a non quarter wavelengthstructure, the optimum thickness was calculated on a computer using thenon-classical approach in an attempt to minimize the mean reflectanceand the results are disclosed by curve 122. The design in TABLE 15 againis basically a classical quarter wavelength three layer structure whereone of the layers is replaced by an optically equivalent three layerconfiguration.

As can be seen in comparison with the above examples of the prior art,the present invention provides a new concept in designing four layeranti-reflective coatings by adopting a non quarter wavelength designapproach that accommodates a remarkable degree of freedom in variationsof the refractive index of the evaporated material and thereby providesa great advantage in the selection of evaporatable materials. Inaddition, it permits a permissible refractive index error duringmanufacturing while still permitting the production of a commercialcoating.

A workable range of optical thicknesses within the broad designparameters of the present invention has been found to be:

0.260 Md, 0.230 A.)

0.520 N d, 0.400 A 0.360 M N d 0.150 )t 0.470 t d, 0.060 x,

In the present invention the first and fourth layers of coating willgenerally have a refractive index range between l.35 and 1.62. Some ofthe materials which are capable of being utilized on the first andfourth layers with their refractive indices in parentheses are MgF,(1.385), SiO, (1.46), ThF (1.5), LaF, (1.56), N33. (AlF4) (1.35), A1 0(1.65 1.56), and CeF (1.62).

The second layer relative to the top of the antireflection coating has arelatively high refractive index generally equal to or between NH 2.00and 2.30. A number of materials can be utilized and illustrative of suchmaterials are the following with their index ofrefractions inparentheses: CeO, (2.30 2.00), ZrO (2.10 2.00), TiO, (2.30 2.00), Ta,0,(2.30 2.00), ZnS (2.30 2.20), and Th0: (2.20 2.00).

Finally, the third layer from the top of the antireflection coating willhave a refractive index equal to or between NM 1.72 and 1.56, andillustrative of the materials which can be utilized are the followingwith their index of refraction in parentheses: A1 0,, (1.65 1.56), MgO(1.72), CeF (1.62), LaF (1.59), NdF (1.60), BeO (1.60), ThOH 1.70), lnO,(1.8-1.9) and a mixture of MgO and A1 0 (1.72 1.65).

The optical thickness of the layer is normally described in fractions ofwavelengths of the light for which the coating is to be used. The rangeof optical thickness for the present invention is set forth as follows:

0.260 x, N d, 0.230

0.520 A N d 0.400 A 0.500 x, N 4, 0.060 x,

0.500 x Md. 0.060 t where N refers to the index of refraction and drefers to the physical thickness while the sub number refers to thecoating layer with the fourth layer being closest to the substrate andthe first layer being furtherest away. The symbol 1. refers to thedesign wavelength which will be within the wavelength band of 400 to 700nanometers and as an illustrative example may be 510 nanometers. Theoptical thickness of the third and fourth layers are set forth in theabove optical thickness table over their broad applicable range;however, as a result of the non-quarter design approach of the presentinvention, it is possible to offer alternative solutions or designparameters to the third and fourth layers that can be summarized asfollows. When the third layer is thicker than Ari/4, then the fourthlayer will be thinner than A0/4, that is 0.500 M N d 0.250 M and 0.250 AN d, 0.060 M. In the alternative, when the third layer is thinner thanAri/4, then the fourth layer will be thicker than Ari/4, that is 0.250 Nd and 0.50QMA0 N4d4 A0.

The indices of refraction of the four layers and the substrate can benumerically related as follows: N l N N, 1v 1v where N, is the index ofrefraction of the coating layer furthest from the substrate and N, isthe substrate index of refraction.

The coatings can be applied by a vacuum evaporation process.

While the above discloses the preferred embodiments of the presentinvention, it should be understood that various modifications arepossible within the scope of this invention by workers skilled in theart and accordingly the invention should be measured solely from thefollowing claims.

What is claimed is:

l. A multi-layered anti-reflection coating for use with a substrate toreduce reflectance of light comprising at least four layers of material,the first layer furthest from the substrate having an optical thicknessof a preselected design wavelength, A.,, in the range of 0.260 M N 1 d,0.230 A0 and an index of refraction in the range of 1.35 to 1.62; thesecond layer having an optical thickness in the range of 0 5 20 A 2 N d0. 4 Q0 1. and an index of refraction in the range of 2.00 to 2.30; theoptical thickness of one of the third and fourth layers is in the rangeof 0.500 1. N d 0.250 A0 while the optical thickness of the other layerof the third and fourth layers is in the range of 0.250 1.0 N d 0.060 Athe third layer has an index of regictio ri n the range of 1.56 to 1.72and the fourth layer closest to the substrate has an index of refractionin the range of 1.35 to 1.62 wherein N refers to the index of refractionand d refers to the physical thickness of the layer.

2. A multi-layered anti-reflection coating as in claim 1 wherein thesubstrate has an index of refraction of N, and the indices of refractionare related as follows, N equals N and N is greater than N; and N,.

3. A multi-layered anti-reflection coating as in claim 1 wherein thefirst and fourth coating layers are selected from the group consistingof MgF,, S10 ThF,,

LaFg, Na3(AlF4), A1203, and ceFa.

4. A multi-layered anti-reflection coating as in claim 1 wherein thesecond coating layer is selected from the group consisting of CeO ZrO,,TiO Ta O ZnS and Th0,.

5. A multi-layered anti-reflection coating as in claim 1 wherein thethird coating layer is selected from the group consisting of A1 0 MgO,CeF LaF NdF BeO, lnO,, ThOH, and a mixture of MgO and A1 0 6. Amulti-layered anti-reflection coating as in claim 1 wherein the firstand fourth coating layer are selected from the group consisting of MgFSiO,, ThF LaF,, Na (AlF.), A1 0 and CeF the second coating layer isselected from the group consisting of CeO,, ZrO,, TiO Ta,0,, ZnS andTh0,, and the third coating layer is selected from the group consistingof A1 0 MgO, CeF LaF NdF BeO, lnO ThOH and a mixture of MgO and A1 0 7.A multi-layered anti-reflection coating as in claim 6 wherein thesubstrate is a glass having an index of refraction N, in the range of1.42 to 1.72.

8. A multi-layered anti-reflection coating for use with a substrate toreduce reflection of energy comprising four layers of material, eachlayer having an optical thickness of a preselected design wavelength Mas follows:

0.260 M N d, 0.230 M 0.520 x N 1, 0.400 A0 0.500 in N 1. 0.060 A whereinN refers to the index of refraction and a refers to the physicalthickness of the layer, the subnumbers corresponding to the layers withN d being the layer furthest from the substrate, the optical thicknessof the layers being adjustable to compensate for variations from anydesign N whereby the design reflectance is maintained.

9. A multi-layered anti-reflection coating as in claim 8 wherein thesubstrate has an index of refraction of N, and the indices of refractionare related as follows, N equals N and N is greater than N; and N,.

10. A multi-layered anti-reflection coating as in claim 8 wherein thesubstrate has an index of refraction of N, and the indices of refractionare related as follows:

11. A multi-layered anti-reflection coating as in claim 8 wherein thefirst layer furtherest from the substrate and the fourth layer adjacentthe substrate have an index of refraction in the range of 1.35 to 1.62,the second layer has an index of refraction in the range of 2.00 to 2.30and the third layer has an index of refraction in the range of 1.56 to1.72.

12. A multi-layered anti-reflection coating as in claim 8 wherein theoptical thickness of the third and fourth layers are as follows:

0.500 A N d 0.250 A 0.250 A N,d 0060M.

13. A multi-layered anti-reflection coating as in claim 8 wherein theoptical thickness of the third and fourth layers are as follows:

14. A multi-layered anti-reflection coating as in claim 8 wherein theoptical thickness of the third and fourth layers are as follows:

0.470 Md. 0.060 A 15. multi-layered anti-reflection coating as in claim8 wherein the first and fourth layers are magnesium fluoride.

16. A multi-layered anti-reflection coating as in claim 8 wherein thefirst and fourth coating layers are selected from the group consistingof MgF,, SiO,, ThF LaF- Na (AlF A1 0 and CeF 17. A multi-layeredanti-reflection coating as in claim 8 wherein the second coating layeris selected from the group consisting of CeO,, ZrO,, TiO,, mo ZnS andTh0,.

18. A multi-layered anti-reflection coating as in claim 8 wherein thethird coating layer is selected from the group consisting of Al,O MgO,CeF LaF NdF BeO, lnO,, ThOH, and a mixture of MgO and A1 0 19. Amulti-layered anti-reflection coating as in claim 8 wherein the firstand fourth coating layers are selected from the group consisting of MgFSiO,, ThF LaF Na (AlF A1 0 and ceF the second coating layer is selectedfrom the group consisting of CeO,, ZrO Tio Ta O,, ZnS and Th0,, and thethird coating layer is selected from the group consisting of A1 0 MgO,CeF LaF NdF BeO, 1110,, ThOH and a mixture of MgO and A1 0 20. Amulti-layered anti-reflection coating as in claim 8 wherein thesubstrate is a glass having an index of refraction N in the range of1.42 to 1.72.

k 4! k I l

2. A multi-layered anti-reflection coating as in claim 1 wherein thesubstrate has an index of refraction of Ns and the indices of refractionare related as follows, N1 equals N4 and N2 is greater than N3 and Ns.3. A multi-layered anti-reflection coating as in claim 1 wherein thefirst and fourth coating layers are selected from the group consistingof MgF2, SiO2, ThF4, LaF2, Na3(AlF4), Al2O3, and CeF3.
 4. Amulti-layered anti-reflection coating as in claim 1 wherein the secondcoating layer is selected from the group consisting of CeO2, ZrO2, TiO2,Ta2O5, ZnS and ThO2.
 5. A multi-layered anti-reflection coating as inclaim 1 wherein the third coating layer is selected from the groupconsisting of Al2O3, MgO, CeF3, LaF3, NdF3, BeO, InO2, ThOH2 and amixture of MgO and Al2O3.
 6. A multi-layered anti-reflection coating asin claim 1 wherein the first and fourth coating layer are selected fromthe group consisting of MgF2, SiO2, ThF4, LaF2, Na3(AlF4), Al2O3, andCeF3; the second coating layer is selected from the group consisting ofCeO2, ZrO2, TiO2, Ta2O5, ZnS and ThO2, and the third coating layer isselected from the group consisting of Al2O3, MgO, CeF3, LaF3, NdF3, BeO,InO2, ThOH2 and a mixture of MgO and Al2O3.
 7. A multi-layeredanti-reflection coating as in claim 6 wherein the substrate is a glasshaving an index of refraction Ns in the range of 1.42 to 1.72.
 8. Amulti-layered anti-reflection coating for use with a substrate to reducereflection of energy comprising four layers of material, each layerhaving an optical thickness of a preselected design wavelength lambda oas follows: 0.260 lambda o > N1d1 > 0.230 lambda o 0.520 lambda o >N2d2 > 0.400 lambda o 0.500 lambda o > N3d3 > 0.060 lambda o 0.500lambda o > N4d4 > 0.060 lambda o wherein N refers to the index ofrefraction and d refers to the physical thickness of the layer, thesubnumbers corresponding to the layers with N1d1 being the layerfurthest from the substrate, the optical thickness of the layers beingadjustable to compensate for variations from any design N whereby thedesign reflectance is maintained.
 9. A multi-layered anti-reflectioncoating as in claim 8 wherein the substrate has an index of refractionof Ns and the indices of refraction are related as follows, N1 equals N4and N2 is greater than N3 and Ns.
 10. A multi-layered anti-reflectioncoating as in claim 8 wherein the substrate has an index of refractionof Ns and the indices of refraction are related as follows: N1 N4 < Ns >N3 < N2.
 11. A multi-layered anti-reflection coating as in claim 8wherein the first layer furtherest from the substrate and the fourthlayer adjacent the substrate have an index of refraction in the range of1.35 to 1.62, the second layer has an index of refraction in the rangeof 2.00 to 2.30 and the third layer has an index of refraction in therange of 1.56 to 1.72.
 12. A multi-layered anti-reflection coating as inclaim 8 wherein the optical thickness of the third and fourth layers areas follows: 0.500 lambda o > N3d3 > 0.250 lambda o 0.250 lambda o >N4d4 > 0.060 lambda o.
 13. A multi-layered anti-reflection coating as inclaim 8 wherein the optical thickness of the third and fourth layers areas follows: 0.250 lambda o > N3d3 > 0.060 lambda o 0.500 lambda o >N4d4 > 0.250 lambda o.
 14. A multi-layered anti-reflection coating as inclaim 8 wherein the optical thickness of the third and fourth layers areas follows: 0.360 lambda o > N3d3 > 0.150 lambda o 0.470 lambda o >N4d4 > 0.060 lambda o.
 15. multi-layered anti-reflection coating as inclaim 8 wherein the first and fourth layers are magnesium fluoride. 16.A multi-layered anti-reflection coating as in claim 8 wherein the firstand fourth coating layers are selected from the group consisting ofMgF2, SiO2, ThF4, LaF2, Na3(AlF4), Al2O3, and CeF3.
 17. A multi-layeredanti-reflection coating as in claim 8 wherein the second coating layeris selected from the group consisting of CeO2, ZrO2, TiO2, Ta2O5, ZnSand ThO2.
 18. A multi-layered anti-reflection coating as in claim 8wherein the third coating layer is selected from the group consisting ofAl2O3, MgO, CeF3, LaF3, NdF3, BeO, InO2, ThOH2 and a mixture of MgO andAl2O3.
 19. A multi-layered anti-reflection coating as in claim 8 whereinthe first and fourth coating layers are selected from the groupconsisting of MgF2, SiO2, ThF4, LaF2, Na3(AlF4), Al2O3, and CeF3; thesecond coating layer is selected from the group consisting of CeO2,ZrO2, TiO2, Ta2O5, ZnS and ThO2, and the third coating layer is selectedfrom the group consisting of Al2O3, MgO, CeF3, LaF3, NdF3, BeO, InO2,ThOH2 and a mixture of MgO and Al2O3.
 20. A multi-layeredanti-reflection coating as in claim 8 wherein the substrate is a glasshaving an index of refraction Ns in the range of 1.42 to 1.72.